Split a plane into smaller plane objects
Manual and slow approach


Select the object and go into edit mode, using Tab
Subdivide the plane into any number of smaller faces using W -> S repeatedly
Click face select  or do Ctrl + Tab -> F
Proceed to select each face in the plane, the press P + Enter to split the plane into separate objects


UPDATE: Automatic and fast approach

Instead of having to go through each face manually, you can do everything in one sweep like this:


Instead of starting with a plane, create a Grid object with Shift + A -> M -> G. Then go into edit mode, using Tab.
Select all faces with A and do Ctrl + E -> D (edge split). Now all of your faces are disconnected.
Select all faces with A and do P -> L. This separated all the faces by loose parts, into separate objects.